?Nothing is provable'

?Nothing is provable, it?s all in the area of possibility?, says John Forbes Nash Jr, interviews Aditya Sinha.

Given your different approach to problem solving, what’s your definition of mathematical elegance?

I like to take a different approach, a fresh approach. It doesn’t mean the new approach is better. The Pythagorean theorem is an example where the simplest or most traditional proof is not the most elegant. If you take a triangle and arrange four copies so that the inner part is a square and the outer part is also a square, that’s a proof (see illustration). It was used as a symbol for the 2002 Mathematical Congress in Beijing. I think some ancient Chinese had thought of this pattern.

I did try to find some comparative elegance when I worked on real algebraic manifolds. In game theory I changed the presentation of the main proof a few times and found a relatively elegant way of presenting it. But the elegant way is not necessarily the guide to scientific knowledge.

After 9/11, why not apply game theory to the war against terrorism?

September 11 became a big thing worldwide in large part because of Washington’s reaction. If they had said these people who committed suicide were really insane, and just made efforts to prepare against and look for insane people like this, things would be different.

Game theory comes in naturally, but the government might not want to say what they are doing. In the US they have the yellow alert, the orange alert, the red alert. But the more of an alert you declare, the more of a cost you add. Extra policemen have to be paid, and they’re not exportable manufactured goods; they simply guard you. And if you declare red alert all the time, people will start to dismiss it. In fact nothing has ever happened when you raise the alerts.

Terrorism is asymmetric, the other side is unknown, and there are a lot of imponderables…

That is very, very natural for game theory. You don’t know what the other side might do. That you don’t know who’s on the other side makes it an unusual form of game theory. In the usual form, you know who’s on the other side, but you don’t know what they’re going to do.

Game theory was applied during the Cold War…That’s when they came up with MAD, mutually assured destruction. It was a concept that full nuclear war between Washington and Moscow would result in tremendous destruction on both sides. A sort of psychological situation, but basically the idea was while it seemed stupid on one side, together with the action of the other cold warrior made war very improbably. That’s what happened.

Does the US government use game theorists while formulating policy?

They might. The RAND corporation used to do that. They could be doing it at West Point, the military college, or at the Naval college at Annapolis. Someone could work out tactics, but it doesn’t necessarily reach into the White House.
Here in India, the prime minister is an economist, so he might know and understand the statistical economics of what he’s doing. Generally you wouldn’t expect a prime minister to have so much of an understanding of economic statistics.

Would you recommend people choose economists as their prime minister?

It has occurred. There was an economist prime minister in Portugal and he didn’t seem to do so greatly.

Does a mathematician’s creativity peak before age 30? Why?

There is a pattern, so it’s frightening to anyone who’s older. Mathematicians can do work fairly young. It doesn’t take long to learn the basics and to learn some specialty. Like Ramanujan, he got things at an early age, he didn’t have many books to study. In other areas you have to do a lot more before you’re ready to get an advanced degree. In experimental physics, it takes a long time to get the experimental work up and going. It’s not likely to occur at an early age. In theoretical physics you don’t have to find a proof of something, but develop an idea, which needs to be tested by experiment.

Once mathematicians get a good reputation and get into teaching, meetings and administration take up some of their time. But the person who proved Fermat’s Last Theorem is the chairman of the department at Princeton, doing administrative work.

Who would be your top five mathematicians of all time?

There’s a Japanese encyclopaedia of mathematics, and its index shows that the most quoted mathematician is (Bernhard) Riemann, certainly a distinguished figure. On the other hand, the one with the largest collected works is (Leonhard) Euler, the Swiss mathematician. I used to think he wasn’t so great because he wasn’t a deep-type of mathematician, but on the other hand, he was very good, so maybe he is the greatest mathematician.Then there’s (Carl Friedrich) Gauss, (Pierre de) Fermat and (Isaac) Newton, though maybe he gets too much credit.

Who invented calculus, Newton or Leibniz?

Leibniz invented the notation we actually use, but Newton’s notation is sometimes used.

Is String Theory the Holy Grail?

I’m very close to the centre of string theory. It would not be wise to express a positive or negative opinion. I consider it something not extremely probable but possible. It involves 11-dimensional equations that are not provable.Nothing is provable. Right now there is no provable truth, it’s all in the area of possibility.